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Clayton R. Featherstone
Job Market Candidate
Ph.D., Stanford, 2010
Post-doctoral Fellow, Harvard Business School
Baker Library 437
Soldiers Field
Boston, MA 02163
214-673-2800
[email protected]
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Working Papers
Rank Efficiency: Investigating a Widespread Ordinal Welfare Criterion
(JOB MARKET PAPER)
Many institutions that allocate scarce goods based on rank-order preferences gauge the success of their
assignments by the resulting rank distributions, that is, how many participants get their first choice,
how many get their second choice, and so on. For example, San Francisco Unified School District, Teach
for America, and Harvard Business School all evaluate assignments in this way. Preferences over rank
distributions capture the practical (but non-Paretian) intuition that hurting one agent to help others might
be desirable. Motivated by this, call an assignment rank efficient if its rank distribution cannot feasibly
be stochastically dominated. Rank efficient mechanisms are simple linear programs that can either be solved
all at once by a computer or through an intuitive sequential improvement process where at each step, the
policy-maker executes a potentially non-Pareto-improving trade cycle. Both methods are used in the field.
Rank efficiency also dovetails nicely with previous literature: it is a refinement of ordinal efficiency
(and hence of ex post efficiency). Although rank efficiency is theoretically incompatible with
strategy-proofness, rank efficient mechanisms can admit a truth-telling equilibrium in low information
environments. Preference data from Featherstone and Roth (2011) show that if agents were to truthfully
reveal their preferences, a rank efficient mechanism could significantly outperform commonly considered
alternatives like random serial dictatorship and the probabilistic serial mechanism. Finally, a competitive
equilibrium mechanism like that of Hylland and Zeckhauser (1979) generates a straightforward generalization of
rank efficiency and sheds light on how rank efficiency interfaces with fairness considerations.
Why Do Some Clearinghouses Yield Stable Outcomes? Experimental Evidence on Out-of-Equilibrium Truth-telling
(with Eric Mayefsky)
When matching mechanisms yield unstable assignments, unraveling can lead participants to abandon them. This is thought to explain why,
empirically, the stable Deferred Acceptance (DA) mechanism persists where unstable alternatives, such as priority mechanisms, do not.
Theory, however, tells us that both DA and priority mechanisms can yield unstable matches in incomplete information equilibrium.
Nonetheless, if match participants on the proposed-to side deviate from equilibrium by truth-telling, then DA yields stable outcomes.
In an experiment, we find such behavior under DA (but not under a priority mechanism). This suggests that out-of-equilibrium truth-telling
might help to explain the success of DA.
School Choice Mechanisms under Incomplete Information: An Experimental Investigation
(with Muriel Niederle)
In a treatment in which student preferences are correlated, we show not
only that students strategically manipulate their preference reports under the
old Boston mechanism, but that they also fail to do so in an optimal way. In
another treatment, however, we look at an environment with uncorrelated preferences
where, under the old Boston mechanism, truth-telling is an equilibrium
response to truth-telling, regardless of the underlying cardinal preferences. In
this treatment, Boston elicits the same level of truth-telling as deferred acceptance,
while outperforming it on efficiency (measured from the interim information
set, where each student knows his own preferences, but only the
distribution of others' ordinal preferences). The experimental findings do not
provide support for the use of Boston in real-world situations, but rather provide
a "proof-of-concept" for the idea that non-strategy-proof mechanisms can
perform quite well if they admit truth-telling as an equilibrium.
Trafficking Illegal Goods and Ancient Commerce
(Supplementary appendix)
(with Matthew Elliott)
Illegal goods are trafficked through couriers with whom legal contracts cannot be enforced. We model the problem of these
couriers absconding and focus on a finite horizon problem in which trade cannot be sustained through reputational effects.
Nonetheless, trade remains possible if there are sufficient gains. Optimal schemes have one courier making numerous, but a
finite number of, return trips, being entrusted with bundles of increasing value, and keeping the last. Our model is robust
to (i) punishment, (ii) bonding and (iii) a competitive market for couriers. We discuss implications for interdiction and
how the model fits some ancient trade as well.
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Works in Progress
Deviation from Truth-telling under a Non-Strategy-Proof Mechanism: Assignment of Majors at an Elite Mexican University
(with Alejandrina Salcedo and Rodrigo Barros)
Every year, an elite Mexican university assigns almost 25,000 incoming freshman to majors by the following computerized procedure: strictly
order the students by their high school grade point averages (GPAs) and run serial dictatorship. The mechanism is not strategy-proof, however,
because it only allows students to list two majors. Still, due to the size of the market, each major essentially has a cutoff GPA, and these
cutoffs are relatively stable from year to year. To see if the students are best-responding to these cutoffs, we separately survey them concerning
their true preferences and find that, although students almost universally manipulate their preferences, almost 40% of them fail to play a static
best-response. On average, these students received a major that was 2.5 ranks lower (out of 6.2) on their surveyed list. Finally, we examine the
effect of a decision aid on the likelihood that a student best-responds. Randomly, students were shown either a large table of information concerning
the cutoffs of all majors, or they were shown a customized table which sorted majors into "green light", yellow light" and "red light" majors, based
on the student's GPA. This experimental intervention allows us to determine how much difference simple decision aids can make when agents face seemingly
difficult decisions.
Diversity in School Assignment: Redesigning the Mechanism in San Francisco
(with Atila Abdulkadiroğlu, Parag Pathak, Muriel Niederle, and Alvin E. Roth)
The San Francisco Unified School District has historically emphasized school level diversity along racial and socioeconomic dimensions. A
lawsuit in the late nineties prohibited the explicit use of race in the assignment of students to schools, and resulted in an assignment
system known as the Diversity Index Lottery. This system is non-strategy-proof and yields assignments that can be dominated, both in
terms of students' rankings and the algorithm's own criterion for diversity. Such "double inefficiency"
serves as a warning about what a poorly designed mechanism can do. In March 2010, the SFUSD board voted to change their mechanism to
one based on the top trading cycles algorithm (TTC). In their new mechanism, student priorities at schools are used as parameters that
policy-makers can use to adjust diversity policy from year to year. Our experience in San Francisco leads us to believe that practical school
choice mechanisms must be easily adjusted by the political process without undermining other more fundamental properties, such as efficiency
and strategy-proofness. Finally, we discuss the rationale for choosing TTC over deferred acceptance. With the freedom to choose any priority
orderings, the set of assignments that a policy-maker can generate is almost unrestricted. Under TTC, regardless of the priorities, we are
guaranteed a Pareto optimal assignment. Of course, it is plausible that diversity concerns might require a school district to choose an
assignment that is Pareto inferior for the students. Briefly, we discuss mechanisms that allow for such inefficiency, so long as an increase
in some policy-maker objective compensates for it.
Do Small Interventions Affect Large Decisions? Experimental Evidence from Teach for America
(with Lucas C. Coffman and Judd Kessler)
We investigate how known, successful behavioral nudges fare in a high stakes context - the decision to accept a job. The job offers come from
Teach for America (TFA), a nationwide non-profit that, every year, admits around 8,000 teachers and makes arrangements for them to work in at-risk
public schools for a period of two years. We look at the decision to join TFA by making a small, one-line change to the admissions letter sent to
successful applicants. To provide a baseline for comparison, we run a similar intervention on a much smaller decision: whether or not admits completely
fill out a TFA survey. Results from previous experiments suggest that our interventions will have an effect on the survey decision, but it is unclear
what will happen in the higher-stakes TFA setting.
Large Market Asymptotics as Proxies for Cognitive Difficulty: Experimental Evidence from Multi-Unit Assignment
(with Jacob Leshno)
Several recent papers have shown that non-strategy-proof mechanisms that work well in practice are only non-strategy-proof because of
manipulations whose profitability disappears in the large market limit. We suggest that these asymptotic results can help predict agent's
behavior even in small markets, letting the asymptotic profitability of a manipulation serve as a proxy for the cognitive difficulty of
manipulating. If the profitability of a manipulation asymptotically vanishes, we say it is "hard"; otherwise, it is "easy". We predict that,
holding profitability constant, agents would employ "easy" manipulations but would miss "hard" manipulations. We test our hypothesis in the lab in the context
of multi-unit assignment by using a random serial dictatorship that goes through the dictatorship ordering multiple times. Such mechanisms are
susceptible to both "easy" and "hard" manipulations. When truth-telling is a dominant strategy, we see truth-telling, and when the equilibrium
manipulation is "easy", we see that manipulation. However, when the equilibrium manipulation is "hard" agents manipulate in an erratic way that
is difficult to explain with standard theory. Hence in our context, agents are less likely to manipulate if the gains vanish asymptotically, but
they do not necessarily revert to truth telling.
Strategy-Proof Mechanisms that Deal with Indifferences and Complicated Diversity Constraints: Matching MBAs to Countries at Harvard Business School
(with Alvin E. Roth)
As a part of the core curriculum at Harvard Business School (HBS), all 900 incoming MBAs must conduct a semester-long collaboration with a foreign
company, which culminates in a two week visit. They are assigned to teams of six, and each team is assigned to a specific company; however,
MBAs are only allowed to submit rankings over the 12 countries. This setup presents two challenges for strategy-proof assignment.
First, MBAs are allowed to express indifferences. We develop a practical implementation of random serial dictatorship with
indifferences and show that, relative to the baseline where students are forced to submit strict preferences, we are able to increase the
number of students who are assigned to a true top choice by over 20% (120 students in absolute terms). Dealing with indifferences is thus of great
import for welfare. The second challenge involves constraints on team composition. Teams are not allowed to have one lone representative of a gender,
nor are they allowed to have a lone representative of a section (HBS MBAs are assigned to one of 10 sections for the duration of their graduate work).
Both of these are either-or type constraints. Also, every team must have at least one member with previous product development experience, which is
a floor constraint. Both types of constraints are known to be theoretically difficult in the context of previous matching models; however, we show
that our setup is easily adapted to deal with them. The flexibility of our generalized random serial dictatorship thus shows great promise for other
applications with complicated constraints.
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